Dana helped her dad build a sandbox for her younger sister. The sandbox is shaped like a rectangular prism that is 4 1 2 feet long and 4 feet wide. Dana used bags of sand to fill the sandbox 1 2 of a foot deep. Each bag contains 1 2 of a cubic foot of sand. How many bags of sand did Dana use?

Answer:

$24

Step-by-step explanation:

Ava + her 3 friends = 4 people total.

The bill was $96

To split this evenly among 4 people we can divide the bill by 4.

96/4 = 24

Therefore each person would pay $24.

Hope this helps! :)

Answer:

Yes

Step-by-step explanation:

9 can go into 8397 evenly without any remainders.

Answer:

8397/9= 933

8397 is divisible by 9 if you divide 8397 by 9 and the quotient is an integer. The easiest way to determine if 8397 is divisible by 9 is to calculate the sum of the digits in 8397. If the sum of the digits is divisible by 9, then 8397 is divisible by 9.

8+3+9+7= 27

27 is divisible by 9

Step-by-step explanation:

Answer:

[tex]\frac{12}{49}[/tex]

explanation:

Use the keep change flip method. This consists of literally flipping a fraction to make the denominators alike, allowing for faster solves and multiplication.

[tex]2\frac{1}{3}[/tex] is [tex]\frac{7}{3}[/tex], so flip 7/3 so it is 3/7, matching up with 4/7.

Next, multiply.

4 x 3

7 x 7

4 x 3 is 12. Write 12 as a numerator.

7 x 7 is 49. Write 49 as a denominator.

Therefore, the answer is [tex]\frac{12}{49}[/tex]

Simplifying? We cannot simplify this number due to a lack of factors.

Let the shorter piece be x. The longer piece is 4 times the length of the other, so it is 4x.

4x + x = 160.

5x = 160

x = 32

4x = 128

The length of the shorter piece is x, which is 32.

1750 litres.............50 cars

1960 litres.............n cars

so n x 1750 = 1960 x 50

n = 98000 : 1750

n = 56

56 cars tanks will be filled

Answer:

56

Step-by-step explanation:

1750 divided by 50 to find out how much litres each car gets. =35

so 35 litres per car so divide 1960 by 35. =56

56 cars can be filled

CHECK ANSWER.

the six extra cars so 35 multiplied by 6. =210

1750+210=1960!

Answer:

x = 1 and x = 3

Step-by-step explanation:

Let's solve your system by substitution.

y=2x+1;y=3x

Step: Solvey=2x+1for y:

y=2x+1

Step: Substitute2x+1foryiny=3x:

y=3x

2x+1=3x

2x+1+−3x=3x+−3x(Add -3x to both sides)

−x+1=0

−x+1+−1=0+−1(Add -1 to both sides)

−x=−1

−x

−1

=

−1

−1

(Divide both sides by -1)

x=1

Step: Substitute1forxiny=2x+1:

y=2x+1

y=(2)(1)+1

y=3(Simplify both sides of the equation)

Answer:

x=1 and y=3

The right answer will be both I and II

I. In the effective rate formula, n is equal to one.

II.The nominal rate is 7.918%.

Compound interest is the interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from previous periods.

The formula for the compound interest is given as:

[tex]A=p(1+\dfrac{r}{n})^{nt}[/tex]

Here

A= amonut

P= principle

r=rate of interest

t=time period

n=for how much time compunded

Thus we can see in the question it is compounded annually so n = 1 and the rate is given as 7.918%

Thus the right answer will be both I and II

I. In the effective rate formula, n is equal to one.

II.The nominal rate is 7.918%.

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Answer:

9:22

Step-by-step explanation:

Find the LCM Least common multiple of all three numbers (minutes)

3,4,5  LCM is 60

Divide each one into the LCM

60/3 = 20

60/4 =  15

60/5 =  12

Totals =82

add that to the time 8:00

82 is an Hour and 22 minute so it would be 9:22

I looked at other problems and this is how they solved it.  I hope it helps

Step-by-step explanation:

m = (y2-y1)/(x2-x1)

m = (4-0)/(0-(-8))

m = 4/8

y = mx + c

4 = (4/8)(0) + c

c = 4

Thus, the equation is y = (4/8)x + 4

Answer:

[tex]in standard notation \: 9 { \times 10}^{ - 4} = 0.0009[/tex]

Answer:

The marathon runner runs 1 mile every 10 minutes.

Step-by-step explanation:

9/2 miles is equal to 4.5 miles. 3/4 hours is equal to 45 minutes.

Answer:

tenths

Step-by-step explanation:

the 2 is in the ones place and the 5 is in the hundreds meaning the 3 would be in the tenths

Answer:

x <4

Step-by-step explanation:

hope it helps

for any question comment me ❤❤

Answer:

-15625

Step-by-step explanation:

Hope this helped !! :)

Have a good day.

Answer: One triangle

Step-by-step explanation:

-The triangle's dimensions are defined and fixed.

-Given the fixed dimensions, only one unique triangle can be constructed.

-Hence, only one triangle of the dimensions 7.2cm, 6.9cm and 12.8 cm can be formed.

Answer:

1

Step-by-step explanation:

The correct shape would be a scalene triangle, which can't be bent and twisted and still have the same side lengths.

Answer: 18

Step-by-step explanation:

Answer:

0,6

Step-by-step explanation:

Answer: Y= -7/3x + 6

Answer:

Solving steps:

find the value of y when x = 1

=> y = 8(1)

multiply 8 by 1

=> y = 8

Hey there!

ORIGINAL EQUATION: y = 8x

This one should be quite easy to answer because we already have the value of x. (x = 1) all we have to do is find the y-value and where it is on the number line.

NEW EQUATION: y = 8(1)

SIMPLIFY IT!

y = 8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 32ft²

Step-by-step explanation:

The area of a trapezoid is given by the formula: A = [(b1+b2)/2] x h, where b1 and b2 are the two bases, and h is the height.

In our situation, b1 = 3, and b2 = 5. The height is given as 2.

Plugging these numbers into our formula:

A = (b1+b2)/2 x h

A = [(3+5)/2] x 2

A = (8/2) x 2

A = 4 x 2

A = 8ft²

8ft² is the area of one trapezoid. If Mr. Smith wants to fit 4 of these shapes into the room, the combined area will be 4 x 8 = 32ft².

Have a nice day :)

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x + cos²x = 1

Consider the left side

[tex]\frac{1-tan^2x}{1+tan^2x}[/tex]

= [tex]\frac{1-\frac{sin^2x}{cos^2x} }{1+\frac{sin^2x}{cos^2x} }[/tex] ← multiply numerator/ denominator of the whole fraction by cos²x

= [tex]\frac{cos^2x-sin^2x}{cos^2x+sin^2x}[/tex]

= [tex]\frac{cos^2x-sin^2x}{1}[/tex]

= cos²x - sin²x

= cos²x - (1 - cos²x)

= cos²x - 1 + cos²x

= 2cos²x - 1

= right side , thus proven

[tex]\frac{1 - \tan^2(x)}{1 + \tan^2(x)}\\= \frac{\frac{\cos^2(x)}{\cos^2(x)} - \frac{\sin^2(x)}{\cos^2(x)}}{\frac{\cos^2(x)}{\cos^2(x)} + \frac{\sin^2(x)}{\cos^2(x)}}\\= \frac{\frac{\cos^2(x) - \sin^2(x)}{\cos^2(x)}}{\frac{\cos^2(x) + \sin^2(x)}{\cos^2(x)}}\\= \frac{\cos^2(x) - \sin^2(x)}{\cos^2(x)} \cdot \frac{\cos^2(x)}{\cos^2(x) + \sin^2(x)}\\= \frac{(\cos^2(x) - \sin^2(x)) \cdot \cos^2(x)}{\cos^2(x) \cdot (\cos^2(x) + \sin^2(x))}\\= \frac{\cos^2(x) - \sin^2(x)}{\cos^2(x) + \sin^2(x)}[/tex]

[tex]= \cos^2(x) - \sin^2(x)\\= \cos^2(x) - (1 - \cos^2(x))\\= \cos^2(x) - 1 + \cos^2(x)\\= 2\cos^2(x) - 1[/tex]

Answer:

$560

Step-by-step explanation:

1/5th the original price just means 20%

20% of 700 is 140

700*.20= 140

Since it's 20% off that means subtraction

700-140=560

Hope this helps!

Answer:

The truck will need to make 3 trips.

Step-by-step explanation:

First, we need to find the volume that the truck can carry. Using the dimensions of the truck and the volume formula, we have:

[tex]V=lwh\\V=8.5\times5\times3.5\\V=148.75\text{ ft}^3[/tex]

Since we need to move a total of 400 cubic feet, we will divide that amount by the truckload capacity (volume).

[tex]400 \div 148.75 \approx 2.689[/tex]

In context, he will need to take three truck loads: two loads will be full, and the third will not be full.

The total distance the bird flew in feet is 140 feet

Given the following parameters

The angle of elevation = 30 degrees

Height =  70 feet

total distance the bird flew in feet (D)

Using the SOH CAH TOA identity

sin 30 = 70/D
D = 70/sin30

D = 140eet

Hence  the total distance the bird flew in feet is 140 feet

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Answer:

No, these equations are not parallel.

Step-by-step explanation:

The equation [tex]y=0[/tex] is a vertical line. This equation, in fact, is the y-axis.

The equation [tex]x=0[/tex] is a horizontal line. This equation, in fact, is the x-axis.

These lines are perpendicular, not parallel.

Given :

You decide to run at least 7.5 miles per week during the week to train for the cross-country season in the fall.

During one week, you run 2 miles on Sunday and 2.5 miles on Wednesday.

To Find :

How many more miles, m, do you need to run before the week is over.

Solution :

Total number of miles we travelled till Wednesday :

t = miles run on Sunday + miles run on Wednesday

t = 2 + 2.5 miles = 4.5 miles.

Now, number of miles remaining :

R = Total target - t

R = 7.5 - 4.5 miles

R = 3 miles.

Therefore, we need to run 3 more miles before the week is over.

Hence, this is the required solution.

Answer:

[tex]5(n + 4)^{\frac{3}{2} }[/tex]  

I hope this helps!

Answer:40

Step-by-step explanation: because 70 times 2 = 140 and you add 40 will equal 180 because every triangle equals 180

The measure of angle m<P is 40 degrees

The given triangle is an isosceles triangle where:

m<R = m<Q

Taking the sum of the interior angles, we will have:

m<P + ,m<Q + m<R  = 180

70 + 70 + m<P = 180

m<P = 180 - 140

m<P= 40 degrees

Hence the measure of angle m<P is 40 degrees

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